To graph the function y = x + 3 for the given domain of 0, 1, 2, 3, 4, 5, we can follow these steps:
1. Start by listing the values of the domain (x-values) from 0 to 5.
Domain: {0, 1, 2, 3, 4, 5}
2. Substitute each x-value into the equation y = x + 3 to find the corresponding y-values.
For x = 0: y = 0 + 3 = 3
For x = 1: y = 1 + 3 = 4
For x = 2: y = 2 + 3 = 5
For x = 3: y = 3 + 3 = 6
For x = 4: y = 4 + 3 = 7
For x = 5: y = 5 + 3 = 8
3. Plot the points (x, y) on a coordinate plane using the x-values from the domain and their corresponding y-values.
(0, 3), (1, 4), (2, 5), (3, 6), (4, 7), (5, 8)
4. Connect the plotted points with a straight line. Since the function y = x + 3 is a linear equation, the graph will be a straight line.
The graph should show a line that starts at the point (0, 3) and increases with a slope of 1 (since the coefficient of x is 1) as x increases.
Here is an example of how the graph would look like on a coordinate plane:
|
9 | *
| *
8 | *
| *
7 | *
| *
6 |*
|_______
0 1 2 3 4 5